First of all, let me tell you, I was as disappointed as you might be when I found out that my Xbox 360 won’t play mkv file only because it chooses not to. (maybe because of licensing issues). So, without much hope, I tried to google for some workaround to make it play the mkv files, and here is what I found:

MKV is just an open source and free multimedia container, so like an AVI file, MKV file can contain any type of files in it.

Xbox 360 supports H.264/MPEG-4 AVC encoding profile of upto level 4.1 (but not if it is in mkv container)